Abstract
In this paper, we extend the scalar-valued $B$-semipreinvex functions and vector-valued preinvex functions to the cases of vector-valued $B$-semipreinvex functions in Banach spaces. We investigate some properties for the vector-valued $B$-semipreinvex functions and consider a new class of vector-valued nonsmooth programming problems in which functions are locally Lipschitz. In terms of the Ralph vector sub-gradient, we obtain the generalized Kuhn-Tucker type sufficient optimality conditions and saddle point condition. Also, a generalized Mond-Weir type dual is formulated and some duality theorems are established involving locally Lipschitz $B$-semipreinvex functions for the pair of primal and dual programming. The results presented in this paper generalize some main results of Kuang and Batista Dos Santoset, Osuna-Gomez, Rojas-Medar and Rufian-Lizana.
Citation
Sheng-Lan Chen. Nan-Jing Huang. Mu-Ming Wong. "$B$-SEMIPREINVEX FUNCTIONS AND VECTOR OPTIMIZATION PROBLEMS IN BANACH SPACES." Taiwanese J. Math. 11 (3) 595 - 609, 2007. https://doi.org/10.11650/twjm/1500404746
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